Device for estimating parameters of battery, and estimation method

ABSTRACT

A device for estimating parameters of battery capable of improving, by using simple calculations, estimation accuracy of a parameter and the like of a battery equivalent circuit model will be provided. 
     The device for estimating parameters of battery for estimating the parameter of a battery ( 1 ) includes: a battery equivalent circuit model ( 4 A) including resistance and a capacitor as the parameter; a logarithmic conversion parameter value estimation unit ( 4 B) for sequentially estimating, by using a logarithmic conversion parameter value serving as a state variable obtained by carrying out logarithmic conversion on the parameter, the logarithmic conversion parameter value with a Kalman filter ( 41 ) from a state equation and an output equation, based on a charging/discharging current and a terminal voltage those being detected; and an inverse logarithmic conversion unit ( 4 C) for obtaining, from the logarithmic conversion parameter value, an estimated parameter value serving as an antilogarithm corresponding to the logarithmic conversion parameter value.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Japanese PatentApplication No. 2012-223002 (filed on Oct. 5, 2012), the entire contentsof which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a device for estimating parameters ofbattery (a battery parameter estimation device) capable of sequentiallyestimating a parameter of a battery equivalent circuit model by using aKalman filter, and also to an estimation method of the battery parameterestimation device.

BACKGROUND

An estimation device described in Patent Document 1 set forth below isknown as a conventional estimation device for estimating an internalstate, a parameter and the like of a battery.

This estimation device for estimating the parameter and the like of thebattery detects a charging/discharging current and a terminal voltage ofthe battery and, based on inputs thereof, sequentially estimates theparameter and an open-circuit voltage with a Kalman filter by using abattery equivalent circuit model. A correction state of charge isestimated from the open-circuit voltage and, based on the correctionstate of charge, the charging/discharging current is corrected. Acorrected charging/discharging current is integrated, and a value thusobtained is divided by a full charge capacity value. Thereby, a state ofcharge (SOC: State of Charge) of the battery is obtained moreaccurately.

Estimation of the parameter of the battery equivalent circuit model andthe open-circuit voltage by the Kalman filter as described above so asto estimate the internal state of the battery such as the SOC and astate of health (SOH: State of Health) has been widely carried out byconventional techniques in addition to the Patent Document 1.

In this case, as disclosed in Non Patent Document 1 set forth below, forexample, when a state equation and an output equation of a target systemare affected by disturbance of white noise having a known covariancematrix, a gain matrix that minimizes a mean square state error may beselected. The Kalman filter is known as an observing device used forthis purpose.

In other words, the Kalman filter may carry out an optimal predictionwhen it may be assumed that future values of the disturbance and thenoise are equal to their mean values (i.e., zero).

CITATION LIST Patent Document

-   Patent Document 1: Japanese Patent Application Laid-Open Publication    No. 2012-47580

Non-Patent Document

-   Non-Patent Document 1: “Model prediction control” Jan M.    Maciejowski, translated by Shuichi Adachi and Masaaki Kanno,    published on Jan. 20, 2005 by Tokyo Denki University Press, pp.    72-73

However, the conventional estimation devices for estimating theparameter and the like of the battery as described above have a problemas described below.

That is, the estimation devices for estimating the parameter and thelike of the battery with the Kalman filter that have been conventionallysuggested, including the conventional estimation device as describedabove, consider that the noise of the parameter (a resistor and acapacitor) is the white noise as described above and these parameterthus form a normal distribution.

Even when the parameter was estimated based on the assumption that thenoise of the parameter is the white noise and the parameter form thenormal distribution, the parameter was estimated with some accuracy.

However, the present inventors, through their experiments andmeasurements, found that a value estimated by the above conventionalmethod may significantly deviate from an actual value and, for example,the parameter such as a resistance value possibly takes an unpracticalnegative value.

This may be because of complex chemical reactions of battery operationswhich causes the deviation of the estimation value in a simplifiedcircuit equivalent model.

However, an equivalent circuit model having more resistors andcapacitors carries out complicated operations and thus has extremedifficulty to be used for actual processing.

An object of the present invention, in view of the above problems, is toprovide a battery parameter estimation device that, in estimating theparameter of the battery equivalent circuit model, may improveestimation accuracy of the parameter by using a simple calculation andobtain the parameter approximate to an actual value, and also to providean estimation method of the battery parameter estimation device.

SUMMARY

In order to achieve the above object, a device for estimating parametersof battery according to the first aspect of the present inventionincluding a charging/discharging current detection unit for detecting acharging/discharging current of a battery, a terminal voltage detectionunit for detecting a terminal voltage of the battery, and a batteryequivalent circuit model including a resistor and a capacitor as aparameter,

the device for estimating parameters of battery estimating the parameterby using the battery equivalent circuit model based on thecharging/discharging current detected by the charging/dischargingcurrent detection unit and the terminal voltage detected by the terminalvoltage detection unit, the device for estimating parameters of batteryincludes:

a logarithmic conversion parameter value estimation unit forsequentially estimating, by using a logarithmic conversion parametervalue serving as a state variable obtained by carrying out logarithmicconversion on the parameter, the logarithmic conversion parameter valuewith a Kalman filter from a state equation and an output equation, basedon the charging/discharging current and the terminal voltage those beingdetected; and

an inverse logarithmic conversion unit for obtaining, by carrying outinverse logarithmic conversion on the logarithmic conversion parametervalue, an estimated parameter value serving as an antilogarithmcorresponding to the logarithmic conversion parameter value.

A device for estimating parameters of battery according to the secondaspect of the present invention is the device for estimating parametersof battery according to the first aspect of the present invention,including:

an internal state value estimation unit for estimating an internal statevalue of the battery based on the parameter serving as the antilogarithmobtained by the inverse logarithmic conversion unit.

A device for estimating parameters of battery according to the thirdaspect of the present invention is the device for estimating parametersof battery according to the second aspect of the present invention,wherein

the internal state value is at least one of a state of charge and astate of health of the battery.

An estimation method of a battery parameter according to the fourthaspect of the present invention is an estimation method the batteryparameter for detecting a charging/discharging current and a terminalvoltage of a battery and, based on the charging/discharging current andthe terminal voltage those being detected, estimating a parameter byusing an equivalent circuit model including a resistor and a capacitorserving as the parameter, the estimation method includes:

sequentially estimating, by using a logarithmic conversion parametervalue serving as a state variable obtained by carrying out logarithmicconversion on the parameter, the logarithmic conversion parameter valuewith a Kalman filter from a state equation and an output equation, basedon the charging/discharging current and the terminal voltage those beingdetected; and

obtaining an estimated parameter value serving as an antilogarithmcorresponding to the logarithmic conversion parameter value by carryingout inverse logarithmic conversion on the logarithmic conversionparameter value.

An estimation method of a battery parameter according to the fifthaspect of the present invention is the estimation method of the batteryparameter according to the fourth aspect, wherein

an internal state value of the battery is estimated based on theparameter serving as the antilogarithm obtained by carrying out theinverse logarithmic conversion.

An estimation method of a battery parameter according to the sixthaspect of the present invention is the estimation method of the batteryparameter according to the fifth aspect, wherein

the internal state value is at least one of a state of charge and astate of health of the battery.

According to the device for estimating parameters of battery of thefirst aspect of the present invention, the logarithmic conversionparameter estimation unit carries out the logarithmic conversion on theparameter of the battery equivalent circuit model and thus obtains thelogarithmic conversion parameter value serving as the state value, andthen sequentially estimates the logarithmic conversion parameter valuewith the Kalman filter based on the charging/discharging current and theterminal voltage. The inverse logarithmic conversion unit carries outthe inverse logarithmic conversion on the logarithmic conversionparameter value estimated and thus obtains the parameter serving as theantilogarithm, which is considered as an estimated parameter value.

Therefore, an accuracy of the parameter estimation of the batteryequivalent circuit model may be improved. Also, the parameter may beprevented from taking an unpractical negative value.

According to a device for estimating parameters of battery of the secondaspect of the present invention, the internal state of the battery mayalso be estimated highly accurately.

According to a device for estimating parameters of battery of the thirdaspect of the present invention, the state of charge and the state ofhealth may be estimated highly accurately.

According the estimation method of the parameter of the battery of thefourth aspect of the present invention, the logarithmic conversionparameter value serving as the state variable is obtained by carryingout the logarithmic conversion on the parameter of the batteryequivalent circuit model and sequentially estimated by the Kalman filterbased on the charging/discharging current and the terminal voltage. Theestimated value is subjected to the inverse logarithmic conversion so asto obtain the parameter serving as the antilogarithm, which isconsidered as the estimated parameter value.

Therefore, the accuracy of the parameter estimation of the batteryequivalent circuit model may be improved. Also, the parameter may beprevented from taking an unpractical negative value.

According to the estimation method of the battery parameter of the fifthaspect of the present invention, the internal state of the battery mayalso be estimated highly accurately.

According to the estimation method of the battery parameter of the sixthaspect of the present invention, the state of charge and the state ofhealth may be estimated highly accurately.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a functional block of a batteryparameter estimation device connected to a battery according to oneembodiment of the present invention;

FIG. 2 is a diagram illustrating a battery equivalent circuit model;

FIG. 3 is a diagram illustrating a relation between an open-circuitvoltage and a state of charge of the battery;

FIG. 4 is a diagram illustrating a third order Foster type batteryequivalent circuit model;

FIG. 5 is a diagram illustrating a third order Cauer type batteryequivalent circuit model;

FIG. 6 is a diagram illustrating measurement data of a current, avoltage, and a state of charge when an electric vehicle is driven inpractice;

FIG. 7 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by a normal Kalmanfilter when the third order Foster type battery equivalent circuit modelis used;

FIG. 8 is a diagram illustrating an estimated parameter value of FIG. 7;

FIG. 9 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by a normalized Kalmanfilter when the third order Foster type battery equivalent circuit modelis used;

FIG. 10 is a diagram illustrating an estimated parameter value of FIG.9;

FIG. 11 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by a Kalman filteremploying logarithmic conversion when the third order Foster typebattery equivalent circuit model is used;

FIG. 12 is a diagram illustrating an estimated parameter value of FIG.11;

FIG. 13 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by the normal Kalmanfilter when the third order Cauer type battery equivalent circuit modelis used;

FIG. 14 a diagram illustrating an estimated parameter value of FIG. 13;

FIG. 15 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by the normalizedKalman filter when the third order Cauer type battery equivalent circuitmodel is used;

FIG. 16 is a diagram illustrating an estimated parameter value of FIG.15;

FIG. 17 is a diagram illustrating an estimated state of charge and itserror as a result of simultaneous estimation made by the Kalman filteremploying logarithmic conversion when the third order Cauer type batteryequivalent circuit model is used; and

FIG. 18 a diagram illustrating an estimated parameter value of FIG. 17.

DETAILED DESCRIPTION

Hereinafter, an embodiment of the present invention will be described indetail based on examples illustrated in drawings.

Embodiment 1

Hereinafter, a battery parameter estimation device according toEmbodiment 1 will be described with reference to the accompanyingdrawings.

The battery parameter estimation device according to Embodiment 1 isused for vehicles such as an electric vehicle, a hybrid electricvehicle, and the like. These vehicles include: an electric motor fordriving the vehicle; a battery; and a controller for controlling powersupply (discharge) to the electric motor, regeneration of braking energyfrom the electric motor during braking, and power recovery (charging) tothe battery from an offboard charging equipment.

A charging/discharging current flown to/from the battery changes aninternal state of the battery. Therefore, the internal state ismonitored and estimated by the battery parameter estimation device.Thereby, necessary information such as a remaining battery level isobtained.

As illustrated in FIG. 1, the battery parameter estimation device forestimating the parameter and the like of a battery 1 includes a voltagesensor 2 and a current sensor 3 those connected to the battery 1, astate estimation unit 4, a charge amount calculation unit 5, a state ofcharge calculation unit 6, and a state of health calculation unit 7.

Note that a micro-computer mounted on the vehicle functions as the stateestimation unit 4, the charge amount calculation unit 5, the state ofcharge calculation unit 6, and the state of health calculation unit 7.

The battery 1 according to the present embodiment is a rechargeablebattery (secondary battery) such as, for example, a lithium ion batterybut not limited thereto. Other batteries such as a nickel-metal hydridebattery and the like may be used, as a matter of course.

The voltage sensor 2 detects a voltage between terminals of the battery1, and a terminal voltage value v thus detected is input to the stateestimation unit 4.

The voltage sensor 2 corresponds to a terminal voltage detection unit ofthe present invention.

The current sensor 3 detects an amount of a discharging current forsupplying power from the battery 1 to the electric motor and the like,as well as an amount of a charging current obtained by collectingbraking energy by using the electric motor serving as a generator duringbraking or obtained by charging from the offboard charging equipment. Acharging/discharging current value i thus detected is output as an inputsignal to the state estimation unit 4.

The current sensor 3 corresponds to the charging/discharging currentdetection unit of the present invention.

The state estimation unit 4 includes a battery equivalent circuit model4A of the battery 1, a logarithmic conversion parameter value estimationunit 4B, and an inverse logarithmic conversion unit 4C.

The battery equivalent circuit model 4A is formed by a Foster type RCladder circuit represented by an approximation by a sum of infiniteseries of a parallel circuit of a resistor and a capacitor connectedthereto, or a Cauer type RC ladder circuit represented by anapproximation by continued fraction expansion of a capacitor connectedto the ground between the resistors connected in series. Note that theresistor and the capacitor serve as the parameter of the batteryequivalent circuit model 4A.

The logarithmic conversion parameter value estimation unit 4B includes aKalman filter 41 and obtains a logarithmic conversion parameter valueserving as a state variable by carrying out logarithmic conversion onthe parameter. Then, the logarithmic conversion parameter valueestimation unit 4B, by using the battery equivalent circuit model 4A,sequentially estimates the logarithmic conversion parameter valueobtained as described above and an open-circuit voltage of the battery1, based on the terminal voltage v obtained from the voltage sensor 2and the charging/discharging current i obtained from the current sensor3. In this estimation, that is, the parameter of the battery equivalentcircuit model 4A is subjected to the logarithmic conversion, and thelogarithmic conversion parameter value thus obtained serving as thestate variable is calculated from the state equation and the outputequation.

The open-circuit voltage (OCV: Open Circuit Voltage) estimated by thelogarithmic conversion parameter value estimation unit 4B is output tothe state of charge calculation unit 6 and the state of healthcalculation unit 7.

Note that the Kalman filter 41 includes a design of a model of a targetsystem (the battery equivalent circuit model 4A in the presentembodiment), inputs the same input signal to the model and an actualsystem, and compares outputs thereof. When there is an error betweenthem, the error is multiplied by a Kalman gain and then fed back to themodel. Thereby, the model is corrected to minimize the error between theoutput of the model and the output of the system. The Kalman filter 41repeats this operation so as to estimate the parameter of the model.

The logarithmic conversion parameter value of the battery equivalentcircuit model 4A obtained by the logarithmic conversion parameter valueestimation unit 4B is input to the inverse logarithmic conversion unit4C. The logarithmic conversion parameter value is then subjected toinverse logarithmic conversion, whereby a parameter serving as anantilogarithm corresponding to the logarithmic conversion parametervalue is obtained.

Note that the battery equivalent circuit model 4A, the logarithmicconversion parameter value estimation unit 4B, and the inverselogarithmic conversion unit 4C of the state estimation unit 4 will bedescribed in detail later.

The charging/discharging current value i of the battery 1 detected bythe current sensor 3 is input to the charge amount calculation unit 5.The charging/discharging current value i is sequentially integrated,whereby a charging/discharging amount flowing to/from the battery 1 isobtained, which is then subtracted from a remaining charging amountstored prior to the sequential integrating calculation. Thereby, acharge amount Q currently held by the battery 1 is calculated. Thecharge amount Q is output to the state of health calculation unit 7.

Since the relation between the open-circuit voltage value and the stateof charge is unlikely to be affected by deterioration of the battery 1,the state of charge calculation unit 6 stores relation data such as acharacteristic table, for example, obtained through preliminaryexperiments and the like of the relation. Based on the characteristictable, the state of charge calculation unit 6 estimates the state ofcharge at the time from an open-circuit voltage estimation valueestimated by the state estimation unit 4. The state of charge thusestimated is used to manage the battery 1.

The state of health calculation unit 7 includes a characteristic tableshowing a relation between the charge amount Q and the open-circuitvoltage OCV for each state of health SOH classified into predeterminedranges. Details of the characteristic table is disclosed in, forexample, Japanese Patent Application Laid-Open Publication No.2012-57956 filed by the present applicant.

The open-circuit voltage estimation value estimated by the stateestimation unit 4 and the charge amount calculated by the charge amountcalculation unit 5 are input to the state of health calculation unit 7.The state of health calculation unit 7 calculates to determine the rangeof the state of health SOH into which the open-circuit voltageestimation value and the charge amount are classified, and acorresponding state of health SOH is output.

The following is a detailed description of the state estimation unit 4of the battery parameter estimation device as described above.

First, the battery equivalent circuit model 4A will be described.

A battery model to be estimated is illustrated in FIG. 2.

This model includes the open-circuit voltage OCV, the resistance R₀, andWarburg impedance Z_(w). The OCV is represented by a nonlinear functionof the SOC as illustrated in FIG. 3.

The SOC has a relation with the current i and a full charge capacity(FCC: Full Charge Capacity) that satisfies:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack & \; \\{{\frac{}{t}{SOC}} = \frac{i}{FCC}} & (1)\end{matrix}$

Note that the Warburg impedance Z_(w) is impedance caused by diffusionprocess of lithium ions inside the battery (note that a lithium batteryis used in the present embodiment).

For the impedance, two different approximation models have beenproposed.

A first model is a Foster type circuit for performing approximation witha sum of infinite series, and a second model is a Cauer type circuit forperforming approximation by continued fraction expansion.

Both models are represented by an n-th order linear equivalent circuit.

The following explains these battery models, provided that n=3, forexample.

First, the equivalent circuit model approximated by a third order Fostertype battery equivalent circuit model is illustrated in FIG. 4. In thefigure, R and C represent the resistor and the capacitor, respectively.Each subscript thereof represents an order.

When x, u, and y represent the state variable, the input, and theoutput, respectively,

[Equation 2]

x=[SOC _(v3 v2 v1)]^(T)  (2)

u=i  (3)

y=v  (4)

is satisfied.

Note that each of the v1 to the v3 represents a voltage drop in thecapacitor corresponding to each subscript, and the i represents thecurrent flowing through the entire circuit. Also, the v represents avoltage drop in the entire circuit, and the subscript T on the matrixrepresents its transposed matrix.

At this time, a state space satisfies:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\{{\overset{.}{x}(t)} = {{F_{f}{x(t)}} + {G_{f}{u(t)}}}} & (5) \\{{y(t)} = {{{OCV}({SOC})} + {H_{f}{x(t)}} + {R_{0}{u(t)}}}} & (6) \\{F_{f} = {{diag}\left( {0,{- \frac{1}{C_{3}R_{3}}},{- \frac{1}{C_{2}R_{2}}},{- \frac{1}{C_{1}R_{1}}}} \right)}} & (7) \\{G_{f} = \begin{bmatrix}\frac{1}{FCC} & \frac{1}{C_{3}} & \frac{1}{C_{2}} & \frac{1}{C_{1}}\end{bmatrix}^{T}} & (8) \\{H_{f} = \begin{bmatrix}0 & 1 & 1 & 1\end{bmatrix}} & (9)\end{matrix}$

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack & \; \\{{C_{n} = {{\frac{C_{d}}{2}\mspace{14mu} n} = 1}},2,3} & (10) \\{{R_{n} = {{\frac{8\; R_{d}}{\left( {{2\; n} - 1} \right)^{2}\pi^{2}}\mspace{14mu} n} = 1}},2,3} & (11)\end{matrix}$

is satisfied.

Note that the above equation (5) is the state equation, and the aboveequation (6) is the output equation.

On the other hand, the equivalent circuit model approximated by a thirdorder Cauer type circuit is shown in FIG. 5.

When x, y, and y represent the state variable, the input, and theoutput, respectively,

[Equation 5]

x=[SOC _(v3 v2 v1)]^(T)  (12)

u=i  (13)

y=v  (14)

is satisfied.

Note that each of the v1 to v3 represents the voltage drop in thecapacitor corresponding to each subscript, the i represents the currentflowing through the entire circuit, and the v represents the voltagedrop in the entire circuit.

At this time, the state space satisfies:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack & \; \\{{\overset{.}{x}(t)} = {{F_{c}{x(t)}} + {G_{c}{u(t)}}}} & (15) \\{{y(t)} = {{{OCV}({SOC})} + {H_{c}{x(t)}} + {R_{0}{u(t)}}}} & (16) \\{F_{c} = {- {\begin{bmatrix}0 & 0 & 0 & 0 \\0 & \frac{1}{C_{3}} & \frac{1}{C_{3}} & \frac{1}{C_{3}} \\0 & 0 & \frac{1}{C_{2}} & \frac{1}{C_{2}} \\0 & 0 & 0 & \frac{1}{C_{1}}\end{bmatrix}\begin{bmatrix}0 & 0 & 0 & 0 \\0 & \frac{1}{R_{3}} & 0 & 0 \\0 & \frac{1}{R_{2}} & \frac{1}{R_{2}} & 0 \\0 & \frac{1}{R_{1}} & \frac{1}{R_{1}} & \frac{1}{R_{1}}\end{bmatrix}}}} & (17) \\{G_{c} = \begin{bmatrix}\frac{1}{FCC} & \frac{1}{C_{3}} & \frac{1}{C_{2}} & \frac{1}{C_{1}}\end{bmatrix}^{T}} & (18) \\{H_{c} = \begin{bmatrix}0 & 1 & 1 & 1\end{bmatrix}} & (19)\end{matrix}$

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack & \; \\{{C_{n} = {{\frac{C_{d}}{{4\; n} - 1}\mspace{14mu} n} = 1}},2,3} & (20) \\{{R_{n} = {{\frac{R_{d}}{{4\; n} - 3}\mspace{14mu} n} = 1}},2,3} & (21)\end{matrix}$

is satisfied.

Note that the above equation (15) is the state equation, and theequation (16) is the output equation.

Next, the Foster type battery equivalent circuit model and the Cauertype battery equivalent circuit model are used for simultaneousestimation of a battery state and the parameter by the Kalman filter.

Although an unscented Kalman filter (UKF: Unscented Kalman Filter) isused here, a Kalman filter of a different type may be used.

The UKF approximates a probability distribution by using a weightedsample point referred to as a sigma point and thereby calculates eachweighted transition. In particular, a mean value and variance aftertransition at each sigma point are calculated and added according to theweight.

In this way, the probability distribution after the transition may befurther approximated to a true value, while preventing an excessiveincrease in a calculation amount. Also, since the probabilitydistribution is approximated by using the sigma point instead ofapproximation of the system, there is no restriction on non-linearity ofthe system.

Here, in order to clarify characteristics of the method of the presentinvention by comparing the method of the present invention to othermethods, the following three application methods were attempted.

A first method estimates the parameter as it stands, a second methodestimates a normalized parameter, and a third method is the method ofthe present invention that estimates the logarithmic conversionparameter value.

First, the first method of estimating the parameter as it stands will bedescribed

The Foster type battery equivalent circuit model and the Cauer typebattery equivalent circuit model are rewritten to expansion modelscapable of simultaneously estimating the parameter and the open-circuitvoltage.

That is, as an expansion state variable and an output,

[Equation 8]

z=[SOC _(v3 v2 v1) R ₀ R _(d) C _(d) i] ^(T)  (22)

y=[v i] ^(T)  (23)

is newly defined.

Here, note that the current i as well as the parameters R₀, R_(d), andC_(d) are used as the state variables.

At this time, the Foster type battery equivalent circuit modelsatisfies:

[Equation 9]

{dot over (z)}(t)=f _(f)(z(t))  (24)

y(t)=h _(f)(z(t))  (25)

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack & \; \\{{f_{f}\left( {z(t)} \right)} = \begin{bmatrix}\frac{i}{FCC} \\{{- \frac{25\; \pi^{2}v_{3}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\{{- \frac{9\; \pi^{2}v_{2}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\{{- \frac{\pi^{2}v_{1}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\0 \\0 \\0 \\0\end{bmatrix}} & (26) \\{{h_{f}\left( {z(t)} \right)} = \begin{bmatrix}{{{OCV}({SOC})} + v_{3} + v_{2} + v_{1} + {R_{0}i}} \\i\end{bmatrix}} & (27)\end{matrix}$

is satisfied.

Also, the Cauer type battery equivalent circuit model satisfies:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack & \; \\{{f_{f}\left( {z(t)} \right)} = \begin{bmatrix}\frac{i}{FCC} \\{{- \frac{25\; \pi^{2}v_{3}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\{{- \frac{9\; \pi^{2}v_{2}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\{{- \frac{\pi^{2}v_{1}}{4\; C_{d}R_{d}}} + \frac{2\; i}{C_{d}}} \\0 \\0 \\0 \\0\end{bmatrix}} & (26) \\{{h_{f}\left( {z(t)} \right)} = \begin{bmatrix}{{{OCV}({SOC})} + v_{3} + v_{2} + v_{1} + {R_{0}i}} \\i\end{bmatrix}} & (27)\end{matrix}$

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack & \; \\{{f_{c}\left( {z(t)} \right)} = \begin{bmatrix}\frac{i}{FCC} \\{{- \frac{{165\; v_{3}} + {66v_{2}} + {11v_{1}}}{C_{d}R_{d}}} + \frac{11\; i}{C_{d}}} \\{{- \frac{{42v_{3}} + {42v_{2}} + {7v_{1}}}{C_{d}R_{d}}} + \frac{7\; i}{C_{d}}} \\{{- \frac{{3v_{3}} + {3v_{2}} + {3v_{1}}}{C_{d}R_{d}}} + \frac{3\; i}{C_{d}}} \\0 \\0 \\0 \\0\end{bmatrix}} & (30) \\{{h_{c}\left( {z(t)} \right)} = \begin{bmatrix}{{{OCV}({SOC})} + v_{3} + v_{2} + v_{1} + {R_{0}i}} \\i\end{bmatrix}} & (31)\end{matrix}$

is satisfied.

The expansion models as described above are discretized by using Euler'smethod, Runge-Kutta method, or the like, and estimated by using the UKF.

Next, the second method, i.e., the method of estimating the normalizedparameter will be described.

In a case where the parameter is estimated as it stands as describedabove, a great difference in the orders of the parameters causes aproblem in accuracy of numerical calculation by a computer. In thiscase, since the orders are as follows: R₀ is 10⁻⁴, R_(d) is 10⁻⁴, andC_(d) is 10⁵, in the process of cancellation of the Kalman gain of theUKF, cancellation of significant digits occurs.

In order to solve the above problem, therefore, a normalized UKF isapplied here.

The normalized UKF converts state variables with different orders intostate variables with uniform orders and estimates such new statevariables.

That is, a new state variable z_(N) with uniform orders with respect tothe state variable z of the equation (22) is represented by:

[Equation 13]

z _(N)=[SOC _(v3 v2 v1) R′ ₀ R′ _(d) C′ _(d) i] ^(T)  (32)

and thus estimated.

Note that the N_(R0), the N_(Rd), and the N_(Cd) are normalized factorsrepresented by:

[Equation 14]

R′ ₀ =N _(R) ₀ R ₀ R′ _(d) =N _(R) _(d) R _(d) C′ _(d) =N _(C) _(d) C_(d)  (33)

In this case, the normalized factors are, for example:

[Equation 15]

N _(R) ₀ =10⁴ N _(R) _(d) =10⁴ N _(C) _(d) =10⁻⁵  (34)

When the output remains as the equation (23), the equivalent circuitmodels of the Foster type (equations (24) and (25)) satisfy:

[Equation 16]

ż _(N)(t)=f _(fN)(z _(N)(t))  (35)

y(t)=h _(fN)(z _(N)(t))  (36)

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack & \; \\{{f_{IN}\left( {z_{N}(t)} \right)} = \begin{bmatrix}\frac{i}{FCC} \\{{- \frac{25\; \pi^{2}N_{R_{d}}N_{C_{d}}v_{3}}{4\; C_{d}^{\prime}R_{d}^{\prime}}} + \frac{2\; N_{C_{d}}i}{C_{d}^{\prime}}} \\{{- \frac{9\; \pi^{2}N_{R_{d}}N_{C_{d}}v_{2}}{4\; C_{d}^{\prime}R_{d}^{\prime}}} + \frac{2\; N_{C_{d}}i}{C_{d}^{\prime}}} \\{{- \frac{\pi^{2}N_{R_{d}}N_{C_{d}}v_{1}}{4\; C_{d}^{\prime}R_{d}^{\prime}}} + \frac{2\; N_{C_{d}}i}{C_{d}^{\prime}}} \\0 \\0 \\0 \\0\end{bmatrix}} & (37) \\{{h_{IN}\left( {z_{N}(t)} \right)} = \begin{bmatrix}{{{OCV}({SOC})} + v_{3} + v_{2} + v_{1} + {\frac{R_{0}^{\prime}}{N_{R_{0}}}i}} \\i\end{bmatrix}} & (38)\end{matrix}$

is satisfied.

Note that the Cauer type battery equivalent circuit model (equations(28) and (29)) may be rewritten in a similar manner.

Next, the present invention, i.e., a method of estimating thelogarithmic conversion parameter value used in Embodiment 1 will bedescribed.

Taking the logarithm of the parameter allows, similarly to thenormalized parameter described above, uniformity of the order of theparameters to be estimated.

In this method, the Kalman filter estimates, instead of a state variableX, an exponent Z thereof.

That is, with a Napier number as a base, Z represented by:

[Equation 18]

X=expZ  (39)

is estimated.

With reference to the state variable z in the equation (22), a statevariable z_(L) that takes a natural logarithm of the parameter isrepresented by:

[Equation 19]

z _(L)=[SOC _(v3 v2 v1) R″ ₀ R″ _(d) C″ _(d) i] ^(T)  (40)

and thus estimated, provided that

[Equation 20]

R″ ₀=lnR ₀ R″ _(d)=lnR _(d) C″ _(d)=lnC _(d)  (41)

is satisfied.

Note that, although the natural logarithm is used here, a logarithm withany positive real number other than 1 as the base may be used.

When the output remains as the equation (23), the expansion models (theequations (24) and (25)) of the Foster type battery equivalent circuitmodel is represented by:

[Equation 21]

ż _(L)(t)=f _(fL)(z _(L)(t))  (42)

y(t)=h _(fL)(z _(L)(t))  (43)

provided that

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack & \; \\{{f_{fL}\left( {z_{L}(t)} \right)} = \begin{bmatrix}\frac{i}{FCC} \\{{- \frac{25\; \pi^{2}v_{3}}{4\; {\exp \left( {C_{d}^{''}R_{d}^{''}} \right)}}} + \frac{2\; i}{\exp \left( C_{d}^{''} \right)}} \\{{- \frac{9\; \pi^{2}v_{2}}{4\; {\exp \left( {C_{d}^{''}R_{d}^{''}} \right)}}} + \frac{2\; i}{\exp \left( C_{d}^{''} \right)}} \\{{- \frac{\pi^{2}v_{1}}{4\; {\exp \left( {C_{d}^{''}R_{d}^{''}} \right)}}} + \frac{2\; i}{\exp \left( C_{d}^{''} \right)}} \\0 \\0 \\0 \\0\end{bmatrix}} & (44) \\{{h_{fL}\left( {z_{L}(t)} \right)} = \begin{bmatrix}{{{OCV}({SOC})} + v_{3} + v_{2} + v_{1} + {{\exp \left( R_{0}^{''} \right)}i}} \\i\end{bmatrix}} & (45)\end{matrix}$

is satisfied.

Note that the Cauer type battery equivalent circuit model (equations(28) and (29) may be rewritten in a similar manner.

As described above, the parameter and the open-circuit voltage of thebattery equivalent circuit model may be sequentially and simultaneouslyestimated by the Kalman filter.

The following is a description of results of simulations of the threemethods described above carried out by using actual driving data of theelectric vehicle.

FIG. 6 illustrates measurement data of the current, the voltage, and thestate of charge obtained when the electric vehicle is driven inpractice. The data of the current and the voltage are used withoutchanging, and the parameter and the state of charge are estimatedsimultaneously.

The following six estimation methods were compared with one another.

First, by using the third order Forster type battery equivalent circuitmodel, the following three different simulations were conducted.

(Simulation 1) Results of the simultaneous estimation by a normal UKFare illustrated in FIG. 7 (an upper graph indicates a relation among anelapsed time, the estimated state of charge, and the true value, and alower graph indicates a relation between the elapsed time and an errorof the state of charge) and in FIG. 8 (illustrating changes in theparameters R₀, R_(d), and C_(d) with respect to the elapsed time).

(Simulation 2) Results of the simultaneous estimation by the normalizedUKF are illustrated in FIG. 9 (an upper graph indicates the relationamong the elapsed time, the estimated state of charge, and the truevalue, and a lower graph indicates the relation between the elapsed timeand the error of the state of charge) and in FIG. 10 (illustratingchanges in the parameters R₀, R_(d), and C_(d) with respect to theelapsed time).

(Simulation 3) Results of the simultaneous estimation by the UKF usingthe logarithmic conversion are illustrated in FIG. 11 (an upper graphindicates the relation among the elapsed time, the estimated state ofcharge, and the true value, and a lower graph indicates the relationbetween the elapsed time and the error of the state of charge) and inFIG. 12 (illustrating changes in the parameters R₀, R_(d), and C_(d)with respect to the elapsed time).

Next, by using the third order Cauer type battery equivalent circuitmodel, the following three different simulations were conducted.

(Simulation 4) Results of the simultaneous estimation by the UKF areillustrated in FIG. 13 (an upper graph indicates the relation among theelapsed time, the estimated state of charge, and the true value, and alower graph indicates the relation between the elapsed time and theerror of the state of charge) and in FIG. 14 (illustrating changes inthe parameters R₀, R_(d), and C_(d) with respect to the elapsed time).

(Simulation 5) Results of the simultaneous estimation by the normalizedUKF are illustrated in FIG. 15 (an upper graph indicates the relationamong the elapsed time, the estimated state of charge, and the truevalue, and a lower graph indicates the relation between the elapsed timeand the error of the state of charge) and in FIG. 16 (illustratingchanges in the parameters R₀, R_(d), and C_(d) with respect to theelapsed time).

(Simulation 6) Results of the simultaneous estimation by the UKF usingthe logarithmic conversion are illustrated in FIG. 17 (an upper graphindicates the relation among the elapsed time, the estimated state ofcharge, and the true value, and a lower graph indicates the relationbetween the elapsed time and the error of the state of charge) and inFIG. 18 (illustrating changes in the parameters R₀, R_(d), and C_(d)with respect to the elapsed time).

The following facts may be seen from the above results and simulationresults of other driving patterns.

First, regarding estimation accuracy of the state of charge, there is nomuch difference among the state of charges estimated in the above threemethods. Regarding average estimation accuracy of the state of charge,however, the UKF using the logarithmic conversion is approximately thesame as, or slightly better than, the normalized UKF and better than thenormal UKF. Especially when the normal UKF is used, large spike-likeerrors occurred in places, which are the causes of a reduction in theestimation accuracy.

Regarding estimation accuracy of the parameters, as is apparent from theabove results, the UKF using the logarithmic conversion has the bestestimation accuracy, followed by the normalized UKF and then the normalUKF.

However, since the true value of the parameter is unknown, the validityof the estimated value is determined with an estimated variance value.

That is, when a range of 1σ indicated by broken lines in FIG. 10, FIG.12, FIG. 14, FIG. 16, and FIG. 18 becomes narrow enough, the estimationaccuracy is high. On the other hand, when the range of 1σ indicated bythe broken line expands, the estimation accuracy is not very reliable.

For example, in FIG. 18 illustrating the results of the UKF using thelogarithmic conversion, the ranges of 1σ of all parameters narrow. Onthe other hand, in FIG. 16 illustrating the results of the normalizedUKF, the range of 1σ of a diffusion capacitance C_(d) expands. Also, inFIG. 14 illustrating the results of the normal UKF, the ranges of 1σ ofthe R₀ and the R_(d) expand too much to fit in the figure, and the rangeof 1σ of the C_(d) expands.

From the comparison of the results of the Foster type and the Cauertype, it can be seen that the Foster type has a higher estimationaccuracy of the state of charge than the Foster type, in general. TheCauer type may cause a large error especially at the time of charging.This is considered to be caused by a complicated difference between theequation (24) and the equation (28).

Here, the present invention, i.e., the estimation of the parametersubjected to the logarithmic conversion by the Kalman filter will befurther described.

Assuming that the parameter forms the normal distribution asconventionally assumed, a range of the estimated parameter value (suchas the resistance) expands or narrows during the estimation. As aresult, the parameter takes an unpractical negative value when the rangeexpands, causing a reduction in the estimation accuracy.

On the other hand, the present embodiment is as follows:

Estimation of the parameter subjected to the logarithmic conversionmeans estimation of, instead of the state variable X, the exponentthereof, i.e., Z represented by

[Equation 23]

X=expZ  (46)

The UKF using the logarithmic conversion estimates the value assumingthat the exponent Z has white noise added thereto.

Under this assumption, the original state variable X follows alogarithmic normal distribution instead of the normal distribution.

Thereby, the parameters R₀, R_(d), and C_(d) of the battery areconsidered to be well satisfying the above assumption.

For example, a diffusion resistance R_(d) of the battery is representedby:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack & \; \\{{{R_{d}(T)} \propto \frac{1}{D(T)}} = {\frac{1}{D_{0}}{\exp \left( \frac{E_{a}}{RT} \right)}}} & (47)\end{matrix}$

provided that the T represents absolute temperature, the D represents adiffusion coefficient, the D₀ represents a constant, the E_(a)represents activation energy, and the R represents a gas constant.

In this case, due to ununiformity of a state in the vicinity of anelectrode surface, the absolute temperature T and the activation energyE_(a) may vary. Assuming such variations form the normal distribution,the original diffusion resistance R_(d) forms a logarithmic normaldistribution.

Although the above discussion may not be theoretically perfect, anobtained value is closer to an actual value at least than a valueobtained by assuming that the parameter of the battery form the normaldistribution as conventionally assumed. Also, the parameter such as theresistance is prevented from taking an unpractical negative value.Therefore, the parameter and an estimated value of the internal stateusing the parameter may be accurately estimated.

As described above, the battery parameter estimation device and theestimation method of the battery parameter according to Embodiment 1includes: the logarithmic conversion parameter value estimation unit 4Bfor sequentially estimating, by using the logarithmic conversionparameter value serving as the state variable obtained by carrying outthe logarithmic conversion on the parameter of the battery equivalentcircuit model 4A of the battery 1, the logarithmic conversion parametervalue with the Kalman filter 41 from the state equation and the outputequation based on the charging/discharging current i and the terminalvoltage v those being detected; and the inverse logarithmic conversionunit 4C for obtaining, by carrying out the inverse logarithmicconversion on the logarithmic conversion parameter value, the parameterserving as the true value corresponding to the logarithmic conversionparameter value. Therefore, the estimation accuracy of the parameter ishigher than the conventional techniques. Also, the estimated parameteris prevented from taking an unpractical negative value, thus improvingthe estimation accuracy.

Further, since the estimation accuracy of the parameter may be improved,the internal state (the state of charge, the state of health and thelike) of the battery 1 may also be estimated highly accurately.

Although the present invention has been described based on theembodiment, it is to be understood that the present invention is notlimited thereto but includes different configurations made within thescope of the present invention.

For example, the battery parameter estimation device according to thepresent invention may be used for the estimation of the internal stateof the battery of the electric vehicle and a hybrid vehicle, as well asfor the estimation of an internal state of a battery used in otherapparatuses or systems.

REFERENCE SIGNS LIST

-   1 battery-   2 voltage sensor (terminal voltage detection unit)-   3 current sensor (charging/discharging current detection unit)-   4 state estimation unit-   4A battery equivalent circuit model-   4B logarithmic conversion parameter value estimation unit-   4C inverse logarithmic conversion unit-   41 Kalman filter-   5 charge amount calculation unit-   6 state of charge calculation unit-   7 state of health calculation unit

1. A device for estimating parameters of battery including acharging/discharging current detection unit for detecting acharging/discharging current of a battery, a terminal voltage detectionunit for detecting a terminal voltage of the battery, and a batteryequivalent circuit model including a resistor and a capacitor as aparameter, the device for estimating parameters of battery estimatingthe parameter by using the battery equivalent circuit model based on thecharging/discharging current detected by the charging/dischargingcurrent detection unit and the terminal voltage detected by the terminalvoltage detection unit, the device for estimating parameters of batterycomprising: a logarithmic conversion parameter value estimation unit forsequentially estimating, by using a logarithmic conversion parametervalue serving as a state variable obtained by carrying out logarithmicconversion on the parameter, the logarithmic conversion parameter valuewith a Kalman filter from a state equation and an output equation, basedon the charging/discharging current and the terminal voltage those beingdetected; and an inverse logarithmic conversion unit for obtaining, bycarrying out inverse logarithmic conversion on the logarithmicconversion parameter value, an estimated parameter value serving as anantilogarithm corresponding to the logarithmic conversion parametervalue.
 2. The device for estimating parameters of battery according toclaim 1, comprising: an internal state value estimation unit forestimating an internal state value of the battery based on the parameterserving as the antilogarithm obtained by the inverse logarithmicconversion unit.
 3. The device for estimating parameters of batteryaccording to claim 2, wherein the internal state value is at least oneof a state of charge and a state of health of the battery.
 4. Anestimation method of a battery parameter for detecting acharging/discharging current and a terminal voltage of a battery and,based on the charging/discharging current and the terminal voltage thosebeing detected, estimating a parameter by using an equivalent circuitmodel including a resistor and a capacitor serving as the parameter, theestimation method comprising: sequentially estimating, by using alogarithmic conversion parameter value serving as a state variableobtained by carrying out logarithmic conversion on the parameter, thelogarithmic conversion parameter value with a Kalman filter from a stateequation and an output equation, based on the charging/dischargingcurrent and the terminal voltage those being detected; and obtaining anestimated parameter value serving as an antilogarithm corresponding tothe logarithmic conversion parameter value by carrying out inverselogarithmic conversion on the logarithmic conversion parameter value. 5.The estimation method according to claim 4, wherein an internal statevalue of the battery is estimated based on the parameter serving as theantilogarithm obtained by carrying out the inverse logarithmicconversion.
 6. The estimation method according to claim 5, wherein theinternal state value is at least one of a state of charge and a state ofhealth of the battery.